A sufficient condition for maximum cycles in bipartite digraphs

A sufficient condition for Hamiltonian cycles in bipartite tournaments

We prove a new sufficient conditi()n on degrees for a bipartite tournament to be Hamiltonian, that is, if an n x n bipartite tournament T satisfies the condition dT(u) + dj;(v) ~ n 1 whenever uv is an arc of T, then T is Hamiltonian, except for two exceptional graphs. This result is shown to be best possible in a sense. T(X, Y, E) denotes a bipartite tournament with bipartition (X, Y) and verte...

A sufficient condition for Hamilton cycles in bipartite tournaments

A note on cycles of maximum length in bipartite digraphs

Adamus and Adamus in 2012 proposed the following conjecture: Let D be a bipartite digraph with colour classes X and Y such that |X| = a ≤ b = |Y |. If d+(u)+d−(v) > a+b+2 2 , whenever u and v lie in opposite colour classes and uv / ∈ A(D), then D contains a cycle of length 2a. Adamus and Adamus have proved that this conjecture is true when a = b. In this paper, we show that this conjecture is t...

A Semiexact Degree Condition for Hamilton Cycles in Digraphs

We show that for each β > 0, every digraph G of sufficiently large order n whose outdegree and indegree sequences d+1 6 . . . 6 d + n and d − 1 6 . . . 6 d − n satisfy d + i , d − i > min {i+ βn, n/2} is Hamiltonian. In fact, we can weaken these assumptions to (i) d+i > min {i+ βn, n/2} or d − n−i−βn > n− i; (ii) d−i > min {i+ βn, n/2} or d + n−i−βn > n− i; and still deduce that G is Hamiltonia...

Bipartite Graphs and Digraphs with Maximum Connectivity

Recently, some sufficient conditions for a digraph to have maximum connectivity or high superconnectivity have been given in terms of a new parameter which can be thought of as a generalization of the girth of a graph. In this paper similar results are derived for bipartite digraphs and graphs showing that, in this case, all the known conditions can be improved. As a corollary, it is shown that...